Dynamical susceptibility of spin glasses in the fractal cluster model

Abstract

We study the dynamical susceptibility $\ensuremath{\chi}$ of spin glasses above the critical temperature using a fractal cluster model. We derive scaling relations for the zero-field limit of the real and imaginary parts of $\ensuremath{\chi}$ which are general since they do not depend on a particular relaxation model. Comparison to data on ${\mathrm{Eu}}_{0.4}$${\mathrm{Sr}}_{0.6}$S yields critical exponents in good agreement with independent determinations. We discuss the different criteria which have been used to extract the critical relaxation time ${\ensuremath{\tau}}_{\ensuremath{\xi}}$ from experimental $\ensuremath{\chi}'\mathrm{s}$. The smallness of the ratio $\frac{\ensuremath{\beta}}{\ensuremath{\nu}z}$ between critical exponents in the spin-glass problem justifies the approximations used to interpret and relate experimental data, for example, with the equation ${\ensuremath{\chi}}^{\ensuremath{'}\ensuremath{'}}=\ensuremath{-}\frac{\ensuremath{\pi}d{\ensuremath{\chi}}^{\ensuremath{'}}}{2d\mathrm{ln}\ensuremath{\omega}}$.